Hello fellow Pocket Fivers! As some of you know, I embarked on a quest to play 180 $22 180-man Sit-n-Goes (SNGs) on PokerStars at the beginning of the year and I finished up on Tuesday, February 22. I’ve been posting semi-regular updates over the last six weeks, but for the final update, I decided that a full-blown article would be appropriate. I pitched the article idea to Adam, fully expecting him to be rolling his eyes, but to my surprise, he actually encouraged me to write it. (I believe his exact words were: “yeah, whatever,” which I interpreted to mean, “Yeah! I would love to read about whatever you write!”) <READMORE>

Some of you may be wondering why I decided to do this challenge. The genesis of the idea actually began several years ago when a friend and I were discussing return on investment (ROI) for multi-table tournaments (MTTs). He kept using an example of a tournament with 100 people in it, and if you played it 100 times, then a hypothetical average person would finish in every place exactly once. Of course, the problem is that almost every MTT has a different number of people in it. When PokerStars started offering their 180-man SNGs he saw it as an opportunity to acquire data on a homogenous set of MTTs. So I decided to do it.

So after 180 tournaments, here are the updated numbers that I’ve been posting over the last six weeks:

Played: 180
In the money: 31 (17.22%)
Final tables: 15 (8.33%)
Wins: 4 (2.22%)
Buy-ins: $3,960
Paid: $7,574.40
ROI: 91.27%

Frankly, I’m pleased. Although some others have posted their own numbers and they’re superior to mine, my numbers have turned out better than I feared they might.

Before I get into some statistical analysis, here are some of the observations I’ve made. First and foremost, it is impossible to really say how much I appreciate the PocketFives.com community for their encouragement and support as I did this. From the comments posted in response to my updates, to the players who would say “good luck on the challenge” when we were on a table together, to the people who actually took time to find me at a table to cheer me on, I was sincerely grateful for it all. This is part of what makes PocketFives.com so valuable to me and, I believe, others. There have been psychological studies that document the positive effects that an encouraging community provides to its members, and I hope that everyone appreciates what Adam, Cal, Riley and Lenny continue to do to ensure that PocketFives remains the site they envisioned.

Secondly, 180 MTTs probably represents more MTTs than I played in all last year, or at least it’s close. One thing this exercise has done is really given me confidence when I play in other MTTs. A lot of people have posted that they believe the competition in these 180s is significantly softer than in most MTTs and I think I’d have to agree. On the other hand, any time you’ve got 180 people putting up their own money to compete, that can be a tough field to wade through.

There are some interesting anomalies in the data too. I never came in 2nd, 5th, or 7th. Does that mean that I am a great heads up player, because every time I got to heads up, I won? No, not really. It’s just a case of not enough data. One thing I’m disappointed about is that I never finished in 19th. This is alarming to me because I wanted to be very aggressive on the bubble to accumulate chips. So if I was truly being aggressive on the bubble, there should have at least been a couple of times where that went horribly wrong and I found myself finishing in 19th place. I talked about finishing in 180th in one of my updates. That was fun.

Looking back, there were certainly tournaments where I never caught any cards at all, where the only pair I got was a pair of g’s – as in, “gg underdog.” And there were other tournaments where I tripled up in the first 5 hands or so. I distinctly remember that one of the tournaments I won I never had a pair of aces at all. And there were other tournaments where I had aces several times and busted out early. Basically what I’m saying is that the cards aren’t as important as the player.

Now I’ll get into some of the data, which may be boring for some of you. What can we conclude from these numbers? Well, actually, not too much. It turns out that 180 tournaments probably just isn’t enough data. But we can make some guesses, and that’s what I will do.

Place Finished Number of SNGS

ITM: 31
19-36: 24
37-64: 22
55-72: 23
73-90: 21
91-108: 17
109-126: 16
127-144: 9
145-162: 10
163-180: 7

These are my finishes as divided into “buckets” of 18 places. The first bucket represents being in the money (ITM). As you can see, my results are definitely weighted towards finishing higher rather than lower. That’s good!

That’s nice and all, but what I’m really looking for is a way to determine if these results are just due to random variance, or if I can really expect these kinds of results. To do this, I need to see what the chances are that this set of data falls into the same set of data as another larger hypothetical set of data. Statistics provides us with a way of doing this. I’m going to skip a lengthy explanation (although I know you are all begging for a Stats 101 lecture right now!). But I will give an example using heads up matches. If I play in 100 heads up SNG matches, and I win 70 of them, the standard deviation of wins is given by the square root of trials (100) times win rate (.7) times loss rate (.3). In this case, the standard deviation would be 4.6 wins. Then you can be 95% certain that your true win rate is between two standard deviations above and below your current win rate. In this example, you should expect to win between 61 and 79 wins for every 100 matches. (Eyes throughout the Pocket Fives community are no doubt glazing over at this very moment.)

Here’s another chart:

<TABLE HEIGHT: 12.75pt?><TBODY><TR><TD vAlign=bottom noWrap width=64><SPAN></SPAN>
</TD><TD vAlign=bottom noWrap width=77><SPAN> Trials</SPAN>
</TD><TD vAlign=bottom noWrap width=64><SPAN> Count</SPAN>
</TD><TD vAlign=bottom noWrap width=72><SPAN> Std Dev</SPAN>
</TD><TD vAlign=bottom noWrap width=72><SPAN> Low</SPAN>
</TD><TD vAlign=bottom noWrap width=64><SPAN> High</SPAN>
</TD></TR><TR><TD vAlign=bottom noWrap width=64><SPAN>Win</SPAN>
</TD><TD vAlign=bottom noWrap width=77><SPAN>180</SPAN>
</TD><TD vAlign=bottom noWrap width=64><SPAN>4</SPAN>
</TD><TD vAlign=bottom noWrap width=72><SPAN>2.0</SPAN>
</TD><TD vAlign=bottom noWrap width=72><SPAN>0.0</SPAN>
</TD><TD vAlign=bottom noWrap width=64><SPAN>8.0</SPAN>
</TD></TR><TR><TD vAlign=bottom noWrap width=64><SPAN>Top 3</SPAN>
</TD><TD vAlign=bottom noWrap width=77><SPAN>180</SPAN>
</TD><TD vAlign=bottom noWrap width=64><SPAN>7</SPAN>
</TD><TD vAlign=bottom noWrap width=72><SPAN>2.6</SPAN>
</TD><TD vAlign=bottom noWrap width=72><SPAN>1.8</SPAN>
</TD><TD vAlign=bottom noWrap width=64><SPAN>12.2</SPAN>
</TD></TR><TR><TD vAlign=bottom noWrap width=64><SPAN>FT</SPAN>
</TD><TD vAlign=bottom noWrap width=77><SPAN>180</SPAN>
</TD><TD vAlign=bottom noWrap width=64><SPAN>15</SPAN>
</TD><TD vAlign=bottom noWrap width=72><SPAN>3.7</SPAN>
</TD><TD vAlign=bottom noWrap width=72><SPAN>7.6</SPAN>
</TD><TD vAlign=bottom noWrap width=64><SPAN>22.4</SPAN>
</TD></TR><TR><TD vAlign=bottom noWrap width=64><SPAN>ITM</SPAN>
</TD><TD vAlign=bottom noWrap width=77><SPAN>180</SPAN>
</TD><TD vAlign=bottom noWrap width=64><SPAN>31</SPAN>
</TD><TD vAlign=bottom noWrap width=72><SPAN>5.1</SPAN>
</TD><TD vAlign=bottom noWrap width=72><SPAN>20.9</SPAN>
</TD><TD vAlign=bottom noWrap width=64><SPAN>41.1</SPAN>
</TD></TR></TBODY></TABLE>

From this chart I can say with 95% confidence, that if I were to play another 180 SNGs, I could expect between 0 and 8 wins. That’s not very helpful. Let’s look at top 3 finishes, since that’s where all the money is. I can expect between 2 and 12 top 3 finishes. Not bad, although the 2 is below average. For Final Tables, it’s similar. I can expect between 8 and 22 final tables for another 180 SNGs. And finally, I can confidently expect between 21 and 41 finishes in the money for another 180 SNGs. That’s cool, because even the low end would be above the hypothetical person’s average.

Of course, the nice thing about statistics is that increasing the number of trials really narrows down the possibilities. If (this is a big if, of course) I were able to somehow exactly duplicate these results for another 180 tournaments, here’s the chart that would be produced.

<TABLE cellSpacing=0 cellPadding=0 width=413 border=0><TBODY><TR><TD vAlign=bottom noWrap width=64></TD><TD vAlign=bottom noWrap width=77><SPAN> Trials</SPAN>
</TD><TD vAlign=bottom noWrap width=64><SPAN> Count</SPAN>
</TD><TD vAlign=bottom noWrap width=72><SPAN> Std Dev</SPAN>
</TD><TD vAlign=bottom noWrap width=72><SPAN> Low</SPAN>
</TD><TD vAlign=bottom noWrap width=64><SPAN> High</SPAN>
</TD></TR><TR><TD vAlign=bottom noWrap width=64><SPAN>Win</SPAN>
</TD><TD vAlign=bottom noWrap width=77><SPAN>360</SPAN>
</TD><TD vAlign=bottom noWrap width=64><SPAN>8</SPAN>
</TD><TD vAlign=bottom noWrap width=72><SPAN>2.8</SPAN>
</TD><TD vAlign=bottom noWrap width=72><SPAN>2.4</SPAN>
</TD><TD vAlign=bottom noWrap width=64><SPAN>13.6</SPAN>
</TD></TR><TR><TD vAlign=bottom noWrap width=64><SPAN>Top 3</SPAN>
</TD><TD vAlign=bottom noWrap width=77><SPAN>360</SPAN>
</TD><TD vAlign=bottom noWrap width=64><SPAN>14</SPAN>
</TD><TD vAlign=bottom noWrap width=72><SPAN>3.7</SPAN>
</TD><TD vAlign=bottom noWrap width=72><SPAN>6.7</SPAN>
</TD><TD vAlign=bottom noWrap width=64><SPAN>21.3</SPAN>
</TD></TR><TR><TD vAlign=bottom noWrap width=64><SPAN>FT</SPAN>
</TD><TD vAlign=bottom noWrap width=77><SPAN>360</SPAN>
</TD><TD vAlign=bottom noWrap width=64><SPAN>30</SPAN>
</TD><TD vAlign=bottom noWrap width=72><SPAN>5.2</SPAN>
</TD><TD vAlign=bottom noWrap width=72><SPAN>19.5</SPAN>
</TD><TD vAlign=bottom noWrap width=64><SPAN>40.5</SPAN>
</TD></TR><TR><TD vAlign=bottom noWrap width=64><SPAN>ITM</SPAN>
</TD><TD vAlign=bottom noWrap width=77><SPAN>360</SPAN>
</TD><TD vAlign=bottom noWrap width=64><SPAN>62</SPAN>
</TD><TD vAlign=bottom noWrap width=72><SPAN>7.2</SPAN>
</TD><TD vAlign=bottom noWrap width=72><SPAN>47.7</SPAN>
</TD><TD vAlign=bottom noWrap width=64><SPAN>76.3</SPAN>
</TD></TR></TBODY></TABLE>

From this chart, we can see that even the most pessimistic evaluation of the numbers would conclude that the hypothetical person (I won’t say “I” because I haven’t done it) producing these results must be better than average. In other words, if I played 360 tournaments and won 8 times, then there would be a less than 5% chance that my actual true rate of first place finishes would turn out to be less than 2.4 per 360 tournaments played over an infinite number of tournaments. Make sense? Oh, sure it does.

I’m not a statistics expert (as any statistics expert has probably figured out) so if I’ve made some invalid conclusions here, I’d appreciate any feedback. Again, thanks to everyone who has encouraged me over the last couple of weeks and to all the others who have suffered through my updates! Good luck and see you on the tables.
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